Details

sample532.0ms

Algorithm

intervals

Results

182.0ms	39×	body	2560	valid
132.0ms	90×	body	1280	valid
106.0ms	73×	body	640	valid
13.0ms	24×	body	320	valid
7.0ms	18×	body	160	valid
3.0ms	12×	body	80	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	19
3	19
2	17
1	13
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize52.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.3b	(- x (sin x))
1.3b	(- x (tan x))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`associate-/r` `add-cbrt-cube` `add-exp-log` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `div-inv`

Counts

3 → 80

Calls

3 calls:

24.0ms	(/ (- x (sin x)) (- x (tan x)))
10.0ms	(- x (sin x))
17.0ms	(- x (tan x))

series254.0ms

Counts

3 → 9

Calls

3 calls:

108.0ms	(/ (- x (sin x)) (- x (tan x)))
58.0ms	(- x (sin x))
87.0ms	(- x (tan x))

simplify847.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1380
1	372
0	157

prune390.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.2b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
44×	`add-sqr-sqrt`
33×	`times-frac`
18×	`distribute-lft-out--`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
6×	`flip3--` `add-cbrt-cube` `add-exp-log` `associate-/r/` `flip--`
5×	`associate-/r*`
4×	`pow1`
3×	`sub-neg` `distribute-rgt-out--` `diff-log` `div-inv` `associate-/l*`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `frac-sub` `sub-div`

Counts

4 → 94

Calls

4 calls:

14.0ms	(/ (sin x) (- x (tan x)))
73.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
4.0ms	(- x (tan x))
5.0ms	(- x (tan x))

series479.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (sin x) (- x (tan x)))
274.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
68.0ms	(- x (tan x))
60.0ms	(- x (tan x))

simplify689.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
2	1452
1	389
0	177

prune531.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (tan x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))
9.8b	(/ (pow (sin x) 2) (* (- x (tan x)) (- x (tan x))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `add-cbrt-cube` `flip--`
8×	`times-frac` `associate-/r/` `add-cube-cbrt` `associate-/l*`
6×	`unpow-prod-down` `div-exp`
4×	`frac-times` `pow1`
3×	`sub-neg` `diff-log` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow-to-exp` `cbrt-undiv` `associate-l/` `pow-exp` `associate-r/` `unpow2` `sqr-pow`
1×	`clear-num` `associate-/r*` `frac-2neg` `cbrt-unprod` `div-inv`

Counts

4 → 85

Calls

4 calls:

14.0ms	(- x (tan x))
8.0ms	(- x (tan x))
8.0ms	(- x (tan x))
37.0ms	(/ (pow (sin x) 2) (* (- x (tan x)) (- x (tan x))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- x (tan x))
78.0ms	(- x (tan x))
68.0ms	(- x (tan x))
114.0ms	(/ (pow (sin x) 2) (* (- x (tan x)) (- x (tan x))))

simplify739.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1365
1	323
0	146

prune547.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

1.3b	(- x (sin x))
1.3b	(- x (sin x))
1.3b	(- x (tan x))
1.3b	(- x (tan x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
4×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 56

Calls

4 calls:

5.0ms	(- x (sin x))
5.0ms	(- x (sin x))
4.0ms	(- x (tan x))
15.0ms	(- x (tan x))

series276.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- x (sin x))
62.0ms	(- x (sin x))
92.0ms	(- x (tan x))
66.0ms	(- x (tan x))

simplify1.4s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
4	2719
3	883
2	360
1	153
0	76

prune317.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes150.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch166.0ms

Steps

Iters	Range		Point
8	0.00104763160503943	5.1212688054922095	0.02988866558285174
9	-205.8624528279525	-0.0007095347148853646	-1.5696248202346277

simplify5.0ms

Iterations

Iter	Nodes
done	37
1	37
0	33

end0.0ms

sample13.8s

Algorithm

intervals

Results

6.4s	1512×	body	2560	valid
4.6s	2746×	body	1280	valid
1.6s	1928×	body	640	valid
531.0ms	987×	body	320	valid
201.0ms	476×	body	160	valid
60.0ms	351×	body	80	valid